Question

Another min/max. Two intervals, both increasing. No local min or max? Work in reply.

Answer 1

\[f(x)5x^3+3x^5\]
\[f'(x)=15x^2+15x^4\]
\[=15x^2(1+x^2)\]
Critical points are just x=0 from 15x^2, because the second multiplicant (1+x^2) can not equal 0.
So, draw number line:
\[f'(-1)= + * + = +\]
\[f'(1)= + * + = +\]

So, I believe this means there is no local min or max. So if the question is to find local max and min, is my answer to state that there is no local min or max?

Answer 2

your conclusion is correct.

Answer 3

ok good. The situation was different than what I usually see, so I wanted to make sure. Thanks.

Answer 4

yw :)